Re: how

Le 12/06/2024 à 23:04, "Chris M. Thomasson" a écrit :

On 6/12/2024 2:03 PM, Chris M. Thomasson wrote:

On 6/12/2024 1:58 PM, WM wrote:

Le 12/06/2024 à 22:51, "Chris M. Thomasson" a écrit :

On 6/12/2024 1:38 PM, WM wrote:

>
Yes, it is impossible to find a last one before ω.

>
Indeed. You are correct here. There is no last dark number?

>
There is one (think of the first unit fraction) but as it is and remains dark, it cannot be caught.

 I thought there were infinitely many dark natural numbers? If so, how can there possibly be a largest dark number?
 

 You told me that there are indeed infinitely many dark natural numbers, right?
 

Yes. You cannot get to the end because dark numbers have no discernible order.
Fact is: If we assume the existence of ω at the ordinal line, then something must exist before, either dark numbers or nothing. There is no third alternative. Or can you imagine one?
Regards, WM